Transcendence conjectures about periods of modular forms and rational structures on spaces of modular forms

  • Winfried Kohnen


The conjecture is made that the rational structures on spaces of modular forms coming from the rationality of Fourier coefficients and the rationality of periods are not compatible. A consequence would be that ζ(2k-1)/π 2k-1 (ζ(s)=Riemann zeta function;k∈ℕ,k≥2) is irrational or even transcendental.


Modular forms rational structures periods transcendence Riemann zeta function 


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    Bertrand D, Varietes abeliennes et formes lineaires d' integrales elliptiques, in:Sém. de Théorie des Nombres, Paris 1979–80 (ed. M.-J. Bertin), pp. 15–27,Progress in Maths.12 Birkhäuser, Boston-Basel-Stuttgart 1981.Google Scholar
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    Beukers F, Irrationality proofs using modular forms,Soc. Math. de France, Astérisque 147–148 (1987), pp. 271–283.Google Scholar
  3. [3]
    Kohnen W and Zagier D, Modular forms with rational periods, in:Modular Forms (ed. R A Rankin) pp. 197–249, (Chichester: Ellis Horwood) 1984.Google Scholar

Copyright information

© Indian Academy of Science 1989

Authors and Affiliations

  • Winfried Kohnen
    • 1
    • 2
  1. 1.Mathematisches Institut der Universität MünsterMünsterFederal Republic of Germany
  2. 2.Max-Planck-Institut für MathematikBonn 3Federal Republic of Germany

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